Abstract.In handbooks of mathematics and mechanics, known to the author, there are provided ready-made definitions of the scalar product and vector product of vectors. It happens that arriving at the formula on the cosine alpha of the angle contained between two vectors, as shown in the handbook [1], and Lagrange's identity permit delivering the genesis of the both products [2]. And so, determining the formula on the cosine of the angle contained between two vectors leads to the scalar product of those two vectors, and determining the formula on the sine of the angle contained between the two vectors leads to the formulation of the vector product of those vectors.

Received: February 21, 2010

AMS Subject Classification: 26A33

Key Words and Phrases: genesis of the scalar product, genesis of the vector product